The Higgs branch of heterotic ALE instantons

We explore the T-duality web of 6D Heterotic Little String Theories, focusing on flavor algebra reducing deformations. A careful analysis of the full flavor algebra, including Abelian factors, shows that the flavor rank is preserved under T-duality. This suggests a new T-duality invariant in addition to the Coulomb branch dimension and the two-group structure constants. We also engineer Little String Theories with non-simply laced flavor algebras, whose appearance we attribute to certain discrete 3-form fluxes in M-theory. Geometrically, these theories are engineered in F-theory with non-Kähler favorable K3 fibers. This geometric origin leads us to propose that freezing fluxes are preserved across T-duality. Along the way, we discuss various exotic models, including two inequivalent Spin(32)/ℤ2 models that are dual to the same E8 × E8 theory, and a family of self-T-dual models.

T-duality and flavor symmetries in Little String Theories

Ahmed,

Oehlmann,

Ruehle

2024

Bounds and dualities of Type II Little String Theories

Baume,

Oehlmann,

Ruehle

2024

We explore the symmetry structure of Type II Little String Theories and their T-dualities. We construct these theories both from the bottom-up perspective starting with seed Superconformal Field Theories, and from the top-down using F-/M-theory. By exploiting anomaly inflow and unitarity of the LST worldsheet theory, we derive strong conditions on the possible 6D bulk theories and their flavor algebras. These constraints continue to apply if gravity is coupled to the theory. We also study the higher form symmetry structure of these theories and show how they get exchanged under T-duality. Finally, we comment on seemingly consistent bottom-up Little String Theories that cannot be constructed from the top-down approach.

Orthosymplectic quotient quiver subtraction

Bennett,

Hanany,

Kumaran

2024

The technique of orthosymplectic quotient quiver subtraction is introduced. This involves subtraction of an orthosymplectic quotient quiver from a 3d$$ \mathcal{N} $$ N = 4 orthosymplectic quiver gauge theory which has the effect of gauging subgroups of the IR Coulomb branch global symmetry. Orthosymplectic quotient quivers for SU(2), SU(3), G2, and SO(7) are found and derived from Type IIA brane systems involving negatively charged branes for certain 6d$$ \mathcal{N} $$ N = (1, 0) gauge theories. Orthosymplectic quotient quiver subtraction is applied to magnetic quivers for nilpotent orbit closures providing new orthosymplectic counterparts to known unitary quivers. New Coulomb branch constructions are found such as for two height four nilpotent orbit closures of F4 and one of height three. A novel application is to find magnetic quivers and Type IIA brane systems for the 6d$$ \mathcal{N} $$ N = (1, 0) worldvolume theory of two $$ \frac{1}{2}\textrm{M}5 $$ 1 2 M 5 branes on E6 Klein singularity and for 6d$$ \mathcal{N} $$ N = (1, 0) (E6, E6) conformal matter. These give a perturbative Lagrangian realisation to the dynamics of strongly interacting M5 branes. The magnetic quiver for 6d$$ \mathcal{N} $$ N = (1, 0) (E6, E6) conformal matter is star-shaped and can also be interpreted as a magnetic quiver for a class $$ \mathcal{S} $$ S theory specified by SO(26) algebra on a three-punctured sphere.